We're dividing 126637 by 17 
We want to divide 126637 by 17.

Let's proceed to step 1:
1 divided by 17 is 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Grab the next digit (2) from the dividend, add it to 1, then carry on: 12 / 17

Moving on to step 2:
If we divide 12 by 17, we get 0 and a remainder of 12.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 12 leaves us with 12.
Take the next digit (6) from the dividend and append it to 12, then repeat: 126 / 17

Let's proceed to step 3:
126 divided by 17 is 7 with a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
If we subtract 119 from 126, we get 7.
Grab the next digit (6) from the dividend, add it to 7, then carry on: 76 / 17

Advancing to step 4:
If we divide 76 by 17, we get 4 and a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 74.0
Subtract 68 from 76 to get 8.
Append the next digit (3) from the dividend to 8 and continue with: 83 / 17

On to step 5:
17 can be fit into 83 4 times, resulting in a remainder of 15.
Record the quotient 4 as the next digit in the result. 
Result so far: 744.0
Subtracting 68 from 83 leaves us with 15.
Append the next digit (7) from the dividend to 15 and continue with: 157 / 17

Moving on to step 6:
The number 17 fits into 157 9 times, leaving a remainder of 4.
Record the quotient 9 as the next digit in the result. 
Result so far: 7449.0
Subtract 153 from 157 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 7:
17 can be fit into 40 2 times, resulting in a remainder of 6.
Write down 2 as next digit of the result. 
Result so far: 7449.2
Deduct 34 from 40 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 8:
The number 17 fits into 60 3 times, leaving a remainder of 9.
The number 3 becomes the next digit in our result. 
Result so far: 7449.23
If we take 51 away from 60, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 9:
When dividing 90 by 17, we get 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 7449.235
Subtracting 85 from 90 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 10:
If we divide 50 by 17, we get 2 and a remainder of 16.
The next digit of our result is 2. 
Result so far: 7449.2352
The remainder is 16 after subtracting 34 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 11:
The number 17 fits into 160 9 times, leaving a remainder of 7.
Put 9 as the next digit of the answer. 
Result so far: 7449.23529
If we subtract 153 from 160, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 12:
When dividing 70 by 17, we get 4 with a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 7449.235294
Subtract 68 from 70 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 13:
The number 17 fits into 20 1 times, leaving a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 7449.2352941
If we subtract 17 from 20, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 14:
The number 17 fits into 30 1 times, leaving a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 7449.23529411
Subtract 17 from 30 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The final outcome is 7449.23529411, with a leftover of 1.3e-08.